Solve for $x$ and $y$ using elimination. ${x+3y = 10}$ ${-x-5y = -14}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-2y = -4$ $\dfrac{-2y}{{-2}} = \dfrac{-4}{{-2}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x+3y = 10}\thinspace$ to find $x$ ${x + 3}{(2)}{= 10}$ $x+6 = 10$ $x+6{-6} = 10{-6}$ ${x = 4}$ You can also plug ${y = 2}$ into $\thinspace {-x-5y = -14}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(2)}{= -14}$ ${x = 4}$